Known shock absorbers comprise a tube; a piston sealably slidably mounted in the tube and attached to a piston rod, the piston separating a compression chamber from a rebound chamber within the tube; a compression stroke valve mounted on the piston; and a rebound stroke valve mounted on the piston. The compression stroke valve acts as a one way valve to allow flow of fluid from the compression chamber to the rebound chamber through one or more compression flow passages in the piston during the compression stroke of the shock absorber. The rebound stroke valve acts as a one way valve which allows flow of fluid from the rebound chamber to the compression chamber through one or more rebound flow passages in the piston during the rebound stroke of the shock absorber. Typically, the valves comprise a number of discs which cover the flow passages during low speed strokes and which deflect to allow fluid flow during strokes above predetermined speeds. In order to allow fluid to flow between the rebound chamber and the compression chamber during low speed strokes, when the valve discs do not deflect, it is usual practise to form one or more apertures in the piston at the outer edge of the valve discs, or in the outer edge of the valve discs. These apertures open into the flow passages and the chambers to bypass the valve discs to allow fluid flow between the chambers during low speed strokes. Such an arrangement does not differentiate between a low speed rebound stroke and a low speed compression stroke, and will provide substantially the same effect during stroking in either direction.